Construction of Field Algebras with Quantum Symmetry from Local Observables

Abstract

It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantum symmetries and algebras of field operators. For every algebra $\A$ of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field operators are obtained which act on a positive definite Hilbert space of states and transform covariantly under the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation relations, these fields are demonstrated to obey local braid relation.

50 pages, HUTMP 93-B333

References in corpus (1)

• Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory

Cited by in corpus (6)

• Combinatorial quantization of the Hamiltonian Chern-Simons theory I
• Quantum groups and nonabelian braiding in quantum Hall systems
• Combinatorial Quantization of the Hamiltonian Chern-Simons Theory II
• An Introduction to Conformal Field Theory
• Lectures on conformal field theory and Kac-Moody algebras
• Quantum Groups as Global Symmetries